NO.PZ202410180200002403
问题如下：
Evaluate Patel’s ability to generate his retirement needs in 10 years after accounting for the effects of inflation on his small business income and his securities portfolio value
选项：
解释：
Patel requires EUR200,000 of real purchasing power throughout retirement. His pension income will adjust for inflation, so this amounts to EURS0,000 of real income. So, he needs EURlS0,000 of real income from his securities portfolio and his small business income. The effects of inflation on his small business income are as follows if it remains at a nominal amount of EUR120,000 per year: Real business income in 10 years = 120,000 x (1 - 0.05)^10 = 71,848 So, in 10 years, the inflation of 5% annually is expected to reduce the purchasing power of Patel's small business income to EUR71,848. Deducting this amount from EURlS0,000 gives a subtotal of EUR78,152. Can the securities portfolio provide this amount of income in 10 years? Applying the following formula to the value of the securities portfolio:
FVIF tx,inflation==[l + r (1-tx）］^T— (1 —π）^ T=[1 + 0.065 (1 — 0)] ^10— (1 — 0.05) ^10 = 1.27840
Multiplying this amount by the current portfolio value of EUR4 million gives EURS,113,600. The securities portfolio generates a 2% pretax cash distribution taxed annually at a 40% rate; thus, the after-tax distribution is 1.2% of the portfolio value. Cash distribution in real terms in 10 years = 0.012 x 5,113,600 = EUR61,363 Thus, Patel faces an income shortfall in 10 years ofEUR16,789 (= 78,152— 61,363). To cover the shortfall, Patel may have to consider liquidating small portions of his securities portfolio to generate additional cash flow each year. Of course, such reductions will cause a decline in the value of his portfolio, thus also reducing future cash distributions from the portfolio, so these would have to be considered as well.
答案里FVIF tx,inf = [1+r(1-tx)]^T-(1-inf)^T中，我理解是把通货膨胀作为了减项，但是为什么公式里还要有（1-tx）的部分呢？我看答案是假设tx为0，这里可以怎么理解呢
